Answer to the Ultimate Question of Life, the Universe, and Everything
#include <stdio.h>
#include <sys/random.h>
#include <stdlib.h>
#include <gmp.h>
/**
* This program simulates a 2D quantum field inspired by ideas from quantum gravity
* and topological quantum field theory (TQFT). Think of it like a grid where each
* point represents a little quantum state with its complex field, energy, and
* some topological charge (basically a fancy number between -1 and 1). The fun
* part is watching how these fields evolve, interact, and distribute energy
* across the whole grid.
*
* We're using a grid to represent space-time. Each point (or cell) evolves based
* on its own quantum state and the states of its neighbors. This is similar to
* lattice gauge theory, where you break up continuous quantum fields into little
* chunks so we can simulate them on a computer.
*
* Each point has a quantum field, which is just a complex number (real and
* imaginary parts). These fields control the energy at each point. The fields
* evolve recursively, which means they change based on nearby points and
* sometimes even points far away due to quantum entanglement.
*
* Every point on the grid has a topological charge, which is a number between -1
* and 1. This charge acts as an invariant and affects how the quantum fields
* evolve over time. Topological charges are key in theories like TQFT and help
* stabilize the quantum states.
*
* The energy at each point comes from the quantum field's magnitude (|φ|²). The
* field evolves through a recursive, fractal-like process. This makes the system
* behave in complex, sometimes chaotic ways. There's also a small chance that
* points far away from each other interact, kind of like how quantum entanglement
* works.
*
* To prevent the energy from becoming uncontrollable, we use a technique called
* renormalization. This process redistributes the energy across the grid,
* ensuring a balanced and stable energy distribution.
*
* There's also an optional energy normalization step that makes sure the total
* energy stays within a reasonable range as the system evolves.
*
* Probably not scientifically accurate, but it's a fun way to play with quantum
* field theory concepts and fractal recursion.
**/
// Quantum lattice size
// Note: The larger the grid size, the slower the simulation will be. You better have a good CPU for this...
// Reduce the grid size if you want to run this on a potato.
#define GRID_SIZE 120
// Number of simulation steps. This is arbitrary though, the important part is the journey, not the destination.
#define TIME_STEPS 10000
// Probability of non-local entanglement
#define NONLOCAL_PROB 0.001
// Renormalization scale
#define RENORM_SCALE 5
// Precision for high-precision arithmetic
#define PRECISION 512
// Small epsilon value to avoid zero division or underflow
#define EPSILON 1e-10
// Enable energy normalization
#define ENABLE_ENERGY_NORMALIZATION 0
// Enable fireworks
#define ENABLE_FIREWORKS 1
// Print state every N time steps
#define REPORT_EVERY 100
// Print quantum field state every N time steps (must be more and multiple of REPORT_EVERY)
#define VISUALS_EVERY 1000
typedef struct {
mpf_t real; // Real part of quantum field (high precision)
mpf_t imag; // Imaginary part of quantum field (high precision)
mpf_t energy_density; // Energy density at this point (high precision)
mpf_t topological_charge; // Topological charge (continuous values)
} QuantumField;
void initialize_field(QuantumField field[GRID_SIZE][GRID_SIZE]) {
for (int i = 0; i < GRID_SIZE; i++) {
for (int j = 0; j < GRID_SIZE; j++) {
mpf_init2(field[i][j].real, PRECISION);
mpf_init2(field[i][j].imag, PRECISION);
mpf_init2(field[i][j].energy_density, PRECISION);
mpf_init2(field[i][j].topological_charge, PRECISION);
// Set random real and imaginary values for the quantum field
// in the range [-10, 10]. This is the initial state of the field and is random.
mpf_set_d(field[i][j].real, rand() / (double) RAND_MAX * 20.0 - 10.0);
mpf_set_d(field[i][j].imag, rand() / (double) RAND_MAX * 20.0 - 10.0);
// Set energy density to a non-zero value
mpf_set_d(field[i][j].energy_density, 10.0);
// Set random continuous topological charge in range [-1, 1]
mpf_set_d(field[i][j].topological_charge, rand() / (double) RAND_MAX * 2.0 - 1.0);
}
}
}
void compute_scaling_factor(const QuantumField *field, mpf_t scaling_factor) {
mpf_t temp;
mpf_init2(temp, PRECISION);
// scaling_factor = 10.0 / (1 + energy_density)
mpf_set_d(temp, 1.0);
mpf_add(temp, temp, field->energy_density);
mpf_set_d(scaling_factor, 10.0);
mpf_div(scaling_factor, scaling_factor, temp);
mpf_mul(scaling_factor, scaling_factor, field->topological_charge);
mpf_clear(temp);
}
// QF evolution function (fractal recursion with hyperloops (the other kind, go away, Elon))
void recursive_evolve( // NOLINT(*-no-recursion)
QuantumField field[GRID_SIZE][GRID_SIZE],
const int x,
const int y,
const int depth,
mpf_t real_res,
mpf_t imag_res
) {
if (depth <= 0) {
mpf_set(real_res, field[x][y].real);
mpf_set(imag_res, field[x][y].imag);
return;
}
const int nx = (x + depth + GRID_SIZE) % GRID_SIZE;
const int ny = (y + depth + GRID_SIZE) % GRID_SIZE;
mpf_t temp_real, temp_imag;
mpf_init2(temp_real, PRECISION);
mpf_init2(temp_imag, PRECISION);
recursive_evolve(field, nx, ny, depth - 1, temp_real, temp_imag);
mpf_t scaling_factor;
mpf_init2(scaling_factor, PRECISION);
compute_scaling_factor(&field[x][y], scaling_factor);
mpf_mul(temp_real, temp_real, scaling_factor);
mpf_mul(temp_imag, temp_imag, scaling_factor);
mpf_add(real_res, field[x][y].real, temp_real);
mpf_add(imag_res, field[x][y].imag, temp_imag);
mpf_clear(temp_real);
mpf_clear(temp_imag);
mpf_clear(scaling_factor);
}
// Quantum gravity-inspired field interaction (non-local + anisotropic effects)
void evolve_field(QuantumField field[GRID_SIZE][GRID_SIZE]) {
for (int i = 0; i < GRID_SIZE; i++) {
for (int j = 0; j < GRID_SIZE; j++) {
// Random recursion depth (min 3, max 5)
const int depth = rand() % 3 + 3;
mpf_t real_res, imag_res;
mpf_init2(real_res, PRECISION);
mpf_init2(imag_res, PRECISION);
recursive_evolve(field, i, j, depth, real_res, imag_res);
mpf_set(field[i][j].real, real_res);
mpf_set(field[i][j].imag, imag_res);
mpf_mul(field[i][j].energy_density, real_res, real_res); // real^2
mpf_t imag_sq;
mpf_init2(imag_sq, PRECISION);
mpf_mul(imag_sq, imag_res, imag_res); // imag^2
mpf_add(field[i][j].energy_density, field[i][j].energy_density, imag_sq);
mpf_clear(real_res);
mpf_clear(imag_res);
mpf_clear(imag_sq);
}
}
}
// Renormalization step to avoid infinities in the quantum field (numerical stabilization)
void renormalize_field(QuantumField field[GRID_SIZE][GRID_SIZE]) {
// This is going to be so fun to decode in a few years...
for (int scale = 1; scale <= RENORM_SCALE; scale++) {
for (int i = 0; i < GRID_SIZE; i += scale) {
for (int j = 0; j < GRID_SIZE; j += scale) {
mpf_t total_real, total_imag, total_energy;
mpf_init2(total_real, PRECISION);
mpf_init2(total_imag, PRECISION);
mpf_init2(total_energy, PRECISION);
// Sum over local fields to renormalize on different scales
for (int dx = 0; dx < scale; dx++) {
for (int dy = 0; dy < scale; dy++) {
const int nx = (i + dx) % GRID_SIZE;
const int ny = (j + dy) % GRID_SIZE;
mpf_add(total_real, total_real, field[nx][ny].real);
mpf_add(total_imag, total_imag, field[nx][ny].imag);
mpf_add(total_energy, total_energy, field[nx][ny].energy_density);
}
}
// Renormalize by averaging the quantum states
mpf_t scale_factor;
mpf_init2(scale_factor, PRECISION);
mpf_set_d(scale_factor, scale * scale);
mpf_div(total_real, total_real, scale_factor);
mpf_div(total_imag, total_imag, scale_factor);
mpf_div(total_energy, total_energy, scale_factor);
// Redistribute the averaged state to all lattice points in the block
for (int dx = 0; dx < scale; dx++) {
for (int dy = 0; dy < scale; dy++) {
const int nx = (i + dx) % GRID_SIZE;
const int ny = (j + dy) % GRID_SIZE;
mpf_set(field[nx][ny].real, total_real);
mpf_set(field[nx][ny].imag, total_imag);
mpf_set(field[nx][ny].energy_density, total_energy);
}
}
mpf_clear(total_real);
mpf_clear(total_imag);
mpf_clear(total_energy);
mpf_clear(scale_factor);
}
}
}
}
// Optionally normalize total energy to conserve energy (see ENABLE_ENERGY_NORMALIZATION)
void normalize_total_energy(QuantumField field[GRID_SIZE][GRID_SIZE], mpf_t initial_total_energy) {
mpf_t current_total_energy, scaling_factor, allowed_fluctuation;
mpf_init2(current_total_energy, PRECISION);
mpf_init2(scaling_factor, PRECISION);
mpf_init2(allowed_fluctuation, PRECISION);
mpf_set_d(current_total_energy, 0.0);
mpf_set_d(allowed_fluctuation, 10); // Allow 10% energy fluctuation. Param?
// Calculate current total energy
for (int i = 0; i < GRID_SIZE; i++) {
for (int j = 0; j < GRID_SIZE; j++) {
mpf_add(current_total_energy, current_total_energy, field[i][j].energy_density);
}
}
// Check if current total energy is within the allowed fluctuation range
mpf_t upper_limit, lower_limit;
mpf_init2(upper_limit, PRECISION);
mpf_init2(lower_limit, PRECISION);
mpf_mul(upper_limit, initial_total_energy, allowed_fluctuation);
mpf_add(upper_limit, upper_limit, initial_total_energy);
mpf_mul(lower_limit, initial_total_energy, allowed_fluctuation);
mpf_sub(lower_limit, initial_total_energy, lower_limit);
if (mpf_cmp(current_total_energy, lower_limit) > 0 && mpf_cmp(current_total_energy, upper_limit) < 0) {
// Total energy is within the allowed fluctuation range, no need to normalize
mpf_clear(current_total_energy);
mpf_clear(scaling_factor);
mpf_clear(allowed_fluctuation);
mpf_clear(upper_limit);
mpf_clear(lower_limit);
return;
}
// scaling_factor = initial_total_energy / current_total_energy
mpf_div(scaling_factor, initial_total_energy, current_total_energy);
// Adjust fields to conserve energy
for (int i = 0; i < GRID_SIZE; i++) {
for (int j = 0; j < GRID_SIZE; j++) {
mpf_mul(field[i][j].energy_density, field[i][j].energy_density, scaling_factor);
mpf_mul(field[i][j].real, field[i][j].real, scaling_factor);
mpf_mul(field[i][j].imag, field[i][j].imag, scaling_factor);
}
}
mpf_clear(current_total_energy);
mpf_clear(scaling_factor);
mpf_clear(allowed_fluctuation);
mpf_clear(upper_limit);
mpf_clear(lower_limit);
}
void visualize_field(QuantumField field[GRID_SIZE][GRID_SIZE]) {
mpf_t max_energy, min_energy, range;
mpf_init2(max_energy, PRECISION);
mpf_init2(min_energy, PRECISION);
mpf_init2(range, PRECISION);
mpf_set_d(max_energy, 0.0);
mpf_set_d(min_energy, 1e10);
for (int i = 0; i < GRID_SIZE; i++) {
for (int j = 0; j < GRID_SIZE; j++) {
if (mpf_cmp(field[i][j].energy_density, max_energy) > 0) {
mpf_set(max_energy, field[i][j].energy_density);
}
if (mpf_cmp(field[i][j].energy_density, min_energy) < 0) {
mpf_set(min_energy, field[i][j].energy_density);
}
}
}
mpf_sub(range, max_energy, min_energy);
char symbols[] = " .:-=+*#%@";
for (int i = 0; i < GRID_SIZE; i++) {
for (int j = 0; j < GRID_SIZE; j++) {
mpf_t normalized_energy;
mpf_init2(normalized_energy, PRECISION);
// Normalize energy density between 0 and 1
mpf_sub(normalized_energy, field[i][j].energy_density, min_energy);
mpf_div(normalized_energy, normalized_energy, range);
int symbol_index = (int) (mpf_get_d(normalized_energy) * (sizeof(symbols) - 2));
symbol_index = symbol_index < 0 ? 0 : symbol_index;
printf("%c", symbols[symbol_index]);
mpf_clear(normalized_energy);
}
printf("\n");
}
mpf_clear(max_energy);
mpf_clear(min_energy);
mpf_clear(range);
}
void simulate_quantum_gravity(QuantumField field[GRID_SIZE][GRID_SIZE]) {
mpf_t initial_total_energy, prev_total_energy;
mpf_init2(initial_total_energy, PRECISION);
mpf_init2(prev_total_energy, PRECISION);
mpf_set_d(initial_total_energy, 0.0);
mpf_set_d(prev_total_energy, 0.0);
for (int i = 0; i < GRID_SIZE; i++) {
for (int j = 0; j < GRID_SIZE; j++) {
mpf_add(initial_total_energy, initial_total_energy, field[i][j].energy_density);
}
}
mpf_set(prev_total_energy, initial_total_energy);
mpf_t energy_change_percentage, energy_diff;
mpf_init2(energy_change_percentage, PRECISION);
mpf_init2(energy_diff, PRECISION);
for (int t = 0; t < TIME_STEPS; t++) {
evolve_field(field);
renormalize_field(field);
if (ENABLE_ENERGY_NORMALIZATION == 1) {
// Normalize total energy to conserve energy
normalize_total_energy(field, initial_total_energy);
}
if (t % 100 == 0) {
mpf_t total_energy, max_energy, min_energy, sum_energy;
mpf_init2(total_energy, PRECISION);
mpf_init2(max_energy, PRECISION);
mpf_init2(min_energy, PRECISION);
mpf_init2(sum_energy, PRECISION);
mpf_set_d(max_energy, 0.0);
mpf_set_d(min_energy, 1e10);
mpf_set_d(sum_energy, 0.0);
int low_count = 0, medium_count = 0, high_count = 0;
for (int i = 0; i < GRID_SIZE; i++) {
for (int j = 0; j < GRID_SIZE; j++) {
if (mpf_cmp(field[i][j].energy_density, max_energy) > 0) {
mpf_set(max_energy, field[i][j].energy_density);
}
if (mpf_cmp(field[i][j].energy_density, min_energy) < 0) {
mpf_set(min_energy, field[i][j].energy_density);
}
mpf_add(total_energy, total_energy, field[i][j].energy_density);
}
}
mpf_t low_threshold, medium_threshold;
mpf_init2(low_threshold, PRECISION);
mpf_init2(medium_threshold, PRECISION);
mpf_sub(energy_diff, max_energy, min_energy); // energy_diff = max_energy - min_energy
mpf_div_ui(energy_diff, energy_diff, 3); // energy_diff /= 3
mpf_add(low_threshold, min_energy, energy_diff); // low_threshold = min_energy + energy_diff
mpf_mul_ui(energy_diff, energy_diff, 2); // energy_diff *= 2
mpf_add(medium_threshold, min_energy, energy_diff);
for (int i = 0; i < GRID_SIZE; i++) {
for (int j = 0; j < GRID_SIZE; j++) {
if (mpf_cmp(field[i][j].energy_density, low_threshold) < 0) {
low_count++;
} else if (mpf_cmp(field[i][j].energy_density, medium_threshold) < 0) {
medium_count++;
} else {
high_count++;
}
}
}
mpf_sub(energy_diff, total_energy, prev_total_energy);
mpf_div(energy_change_percentage, energy_diff, prev_total_energy);
mpf_mul_ui(energy_change_percentage, energy_change_percentage, 100);
mpf_sub(energy_diff, max_energy, min_energy);
// ================== Print simulation information ==================
printf("Time step %d:\n", t);
gmp_printf(" Energy Change from Previous Step: %.5Ff%%\n", energy_change_percentage);
gmp_printf(" Energy Range (Max - Min): ");
gmp_printf("%.E\n", energy_diff);
printf(" Energy Distribution:\n");
printf(" Low energy cells (<0.1): %d\n", low_count);
printf(" Medium energy cells (0.1 - 0.5): %d\n", medium_count);
printf(" High energy cells (>0.5): %d\n", high_count);
// :D
if (ENABLE_FIREWORKS == 1 && low_count == 0 && medium_count == 0) {
printf("Your universe is too excited.....\n");
printf("============================================\n");
printf("============== GAME OVER ===================\n");
printf("============================================\n");
printf("Insert coin to continue \n");
exit(0);
}
// Update the previous total energy for the next loop
mpf_set(prev_total_energy, total_energy);
if (t % VISUALS_EVERY == 0) {
visualize_field(field);
}
// ================== End of simulation information ==================
mpf_clear(total_energy);
mpf_clear(max_energy);
mpf_clear(min_energy);
mpf_clear(sum_energy);
}
}
mpf_clear(initial_total_energy);
mpf_clear(prev_total_energy);
mpf_clear(energy_change_percentage);
mpf_clear(energy_diff);
}
void clear_field(QuantumField field[GRID_SIZE][GRID_SIZE]) {
for (int i = 0; i < GRID_SIZE; i++) {
for (int j = 0; j < GRID_SIZE; j++) {
mpf_clear(field[i][j].real);
mpf_clear(field[i][j].imag);
mpf_clear(field[i][j].energy_density);
mpf_clear(field[i][j].topological_charge);
}
}
}
void seed_random_from_urandom() {
unsigned int seed;
if (getrandom(&seed, sizeof(seed), 0) == -1) {
perror("Failed to get random");
exit(EXIT_FAILURE);
}
srand(seed);
}
int main() {
seed_random_from_urandom();
QuantumField field[GRID_SIZE][GRID_SIZE];
initialize_field(field);
simulate_quantum_gravity(field);
clear_field(field);
return 0;
}